In this paper we propose quasi-optimal error estimates, in various
norms, for the Streamline-Upwind Petrov-Galerkin (SUPG) method applied to the
linear one-dimensional advection-diffusion problem. We follow the classical
argument due to Babuska and Brezzi, therefore the goal of this work is the
proof of the inf-sup and of the continuity conditions for the bilinear
stabilized variational form, with respect to suitable norms. These norms are
suggested by our previous work, in which we analyze the continuous
multi-dimensional advection-diffusion operator. We obtain these results by
means of functional spaces interpolation.